To calculate the horizontal displacement of an object thrown into the air, you need to consider the initial velocity and launch angle. Assuming there is no air resistance, we can use the following formula:
Horizontal displacement = (initial velocity * time of flight * cosine of launch angle)
In this case, the initial velocity is 30 m/s and the launch angle is 28 degrees. To find the time of flight, we can use the vertical motion equation for the maximum height reached by the projectile:
Vertical displacement = (initial velocity * sin launch angle)^2 / (2 * acceleration due to gravity)
Since the object reaches the same vertical displacement on its way up as it does on its way down, we can calculate the time of flight as twice the time it takes to reach the maximum height. The equation for the time it takes to reach the maximum height is:
time to max height = (initial velocity * sin launch angle) / (acceleration due to gravity)
Given that the acceleration due to gravity is approximately 9.8 m/s², we can substitute the values into the formulas:
time to max height = (30 * sin 28) / 9.8 ≈ 1.62 seconds
Now we can calculate the horizontal displacement:
Horizontal displacement = (30 * 1.62 * cos 28) ≈ 41.13 meters
Therefore, the horizontal displacement of the object thrown into the air at a velocity of 30 m/s with an angle of 28 degrees is approximately 41.13 meters.